(x-1)(x-81)=0

Solution for (x-1)(x-81)=0 equation:

Simplifying
(x + -1)(x + -81) = 0

Reorder the terms:
(-1 + x)(x + -81) = 0

Reorder the terms:
(-1 + x)(-81 + x) = 0

Multiply (-1 + x) * (-81 + x)
(-1(-81 + x) + x(-81 + x)) = 0
((-81 * -1 + x * -1) + x(-81 + x)) = 0
((81 + -1x) + x(-81 + x)) = 0
(81 + -1x + (-81 * x + x * x)) = 0
(81 + -1x + (-81x + x2)) = 0

Combine like terms: -1x + -81x = -82x
(81 + -82x + x2) = 0

Solving
81 + -82x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(81 + -1x) = 0

Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve:

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -1x = 0 + -1
-1x = 0 + -1

Combine like terms: 0 + -1 = -1
-1x = -1

Divide each side by '-1'.
x = 1

Simplifying
x = 1
Subproblem 2
Set the factor '(81 + -1x)' equal to zero and attempt to solve:

Simplifying
81 + -1x = 0

Solving
81 + -1x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-81' to each side of the equation.
81 + -81 + -1x = 0 + -81

Combine like terms: 81 + -81 = 0
0 + -1x = 0 + -81
-1x = 0 + -81

Combine like terms: 0 + -81 = -81
-1x = -81

Divide each side by '-1'.
x = 81

Simplifying
x = 81
Solution
x = {1, 81}